<?xml version="1.0" encoding="UTF-8"?>
<solution xmlns="http://geocentral.net">
<version>3.1</version>
<envelope>
<author>
<name>Stelian Dumitrascu</name>
<email>stelian@geocentral.net</email>
<web>http://geocentral.net/geometria</web>
</author>
<comments>Esta solución es parte del almacén o repositorio de Geometria.</comments>
</envelope>
<problem>
<envelope>
<author>
<name>Stelian Dumitrascu</name>
<email>stelian@geocentral.net</email>
<web>http://geocentral.net/geometria</web>
</author>
<comments>Este problema es parte del almacén o repositorio de Geometria.</comments>
</envelope>
<text>Una esfera de un diámetro máximo se coloca en este tazón hecho de un prisma regular unido a una pirámide regular. El tazón estaba inicialmente lleno de agua. ¿Cómo hallar el volumen de agua desplazado por la esfera?</text>
<notepad>
</notepad>
<figures>
<figure>
<name>Tazón</name>
<color>#ffff</color>
<transparent>true</transparent>
<labelled>false</labelled>
<solid>
<points>
<point>
<label>A</label>
<coords>0.996180339887499 0.0 -0.9770271963607354</coords>
</point>
<point>
<label>B</label>
<coords>0.30519733426244633 0.9510565162951535 -0.9770271963607354</coords>
</point>
<point>
<label>C</label>
<coords>-0.8128366544874485 0.5877852522924732 -0.9770271963607354</coords>
</point>
<point>
<label>F</label>
<coords>0.996180339887499 0.0 -0.22702719636073543</coords>
</point>
<point>
<label>D</label>
<coords>-0.8128366544874486 -0.587785252292473 -0.9770271963607354</coords>
</point>
<point>
<label>E</label>
<coords>0.3051973342624461 -0.9510565162951536 -0.9770271963607354</coords>
</point>
<point>
<label>G</label>
<coords>0.30519733426244633 0.9510565162951535 -0.22702719636073543</coords>
</point>
<point>
<label>H</label>
<coords>-0.8128366544874485 0.5877852522924732 -0.22702719636073543</coords>
</point>
<point>
<label>I</label>
<coords>-0.8128366544874486 -0.587785252292473 -0.22702719636073543</coords>
</point>
<point>
<label>J</label>
<coords>0.3051973342624461 -0.9510565162951536 -0.22702719636073543</coords>
</point>
<point>
<label>K</label>
<coords>-0.00381966011250099 0.0 1.4059659654947168</coords>
</point>
</points>
<lines>
</lines>
</solid>
<camera>
<attitude>0.2946608629628241 0.7208393787344641 -0.5807039079065011 0.2373784683703098</attitude>
</camera>
</figure>
</figures>
<answer>
<type>number</type>
<value>4.2732230472552475</value>
</answer>
</problem>
<log>
<action>
<className>GCutAction</className>
<figureName>Tazón</figureName>
<p0Label>H</p0Label>
<p1Label>C</p1Label>
<p2Label>K</p2Label>
<figure1Name>Figura1</figure1Name>
<figure2Name>Figura2</figure2Name>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Figura2</figureName>
<p0Label>K</p0Label>
<p1Label>M</p1Label>
<p2Label>C</p2Label>
</action>
<action>
<className>GDrawBisectorAction</className>
<figureName>Figura2</figureName>
<p0Label>L</p0Label>
<p1Label>M</p1Label>
<p2Label>K</p2Label>
</action>
<action>
<className>GIntersectAction</className>
<figureName>Figura2</figureName>
<p11Label>L</p11Label>
<p12Label>O</p12Label>
<p21Label>K</p21Label>
<p22Label>N</p22Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Figura2</figureName>
<p0Label>P</p0Label>
<p1Label>K</p1Label>
<p2Label>L</p2Label>
</action>
<action>
<className>GMeasureDistanceAction</className>
<figureName>Figura2</figureName>
<p1Label>P</p1Label>
<p2Label>Q</p2Label>
<variableName>Radio</variableName>
</action>
<action>
<className>GLayDistanceAction</className>
<figureName>Figura2</figureName>
<distance>Radio</distance>
<p0Label>P</p0Label>
<p1Label>K</p1Label>
<p2Label>N</p2Label>
</action>
<action>
<className>GMeasureDistanceAction</className>
<figureName>Figura2</figureName>
<p1Label>R</p1Label>
<p2Label>N</p2Label>
<variableName>Altura</variableName>
</action>
<action>
<className>GLayDistanceAction</className>
<figureName>Figura2</figureName>
<distance>Radio</distance>
<p0Label>P</p0Label>
<p1Label>M</p1Label>
<p2Label>C</p2Label>
</action>
<action>
<className>GMeasureDistanceAction</className>
<figureName>Figura2</figureName>
<p1Label>S</p1Label>
<p2Label>T</p2Label>
<variableName>Base</variableName>
</action>
<action>
<className>GCalcEvaluateAction</className>
<variableName>Volumen</variableName>
<expression>PI*Altura*(3*Base^2+Altura^2)/6</expression>
</action>
<action>
<className>GSolutionAnswerAction</className>
<value>Volumen</value>
</action>
</log>
</solution>